There has been proposed a method in which an input digital signal is converted into a corresponding analog signal by filtering a pulse width signal, the pulse width of which depends on a data value of the input digital signal. This method has an advantage of obtaining a high precision of conversion without using any high precision components in a converting circuit. However, if the pulse width signal is improperly produced, there tends to be produced a distortion in a range of high frequency even though the pulse width corresponding to the data value is precisely formed. Also, if the number of bits of the digital signal to be converted increases, the speed of conversion becomes disadvantageously lower.
More particularly, in the prior art, when the input digital signal is converted into the pulse width signal, the pulse width of the pulse width signal is determined on a time interval from the sampling time so that the center of the pulse width of the pulse width signal varies within a sampling period in accordance with the data value of the sampled input digital signal. Therefore, the waveform of the demodulated analog signal through the filter is extended in the portion in which a level increases, in comparison to the corresponding portion of the original analog signal, while it is compressed in the portion in which a level decreases, in comparison to the corresponding portion of the original analog signal. Thus, it will be noted that the waveform of the demodulated analog signal differs from that of the original analog signal, particularly in the range of high frequency.
In order to solve the problem of speed of conversion, there will be considered a method in which a digital signal consists of a combination of upper and lower bits which are divided and processed in parallel with each other in a digital-to-pulse width conversion. The weight ratio between both upper and lower bits is a predetermined value, with the upper bits having a much greater weight of data value of the digital signal. In the digital-to-pulse width conversion of such digital signal, the upper and lower bits are converted into upper and lower pulse width signals, respectively. Thereafter both pulse width signals are mixed after attenuating the lower pulse width signal in accordance with the weight ratio. However, in the digital signal consisting of upper and lower bits, there occurs a moving up from the lower bits to the upper bits or a moving down from the upper bits to the lower bits when the data value of the digital signal increases or decreases, respectively. If an appearing or disappearing time of an increasing or a decreasing portion of the pulse width of the upper pulse width signal due to the moving up or down has an improper relation to a center of the lower pulse width signal disappeared or appeared due to the moving up and down, there will occur a distortion or noise. FIG. 1 shows an occurrence in the distortion when there occurs the moving up to the upper bits. As shown in FIG. 1A, when the moving up to the upper bits occurs, the upper pulse width signal a has a respective increased area of Sa at both ends of the pulse signal while the lower pulse width signal b, which is given the predetermined attenuation disappears. In fact, the increased pulse area of 2Sa is larger by the area corresponding to the minimum unit of the lower pulse width signal that the decreased pulse area of 2Sb in the lower pulse width signal b, but both of the areas 2Sa and 2Sb will be considered to be equal to each other for brief description. As shown in FIG. 1B, when the moving up occurs, pulses a' corresponding to each pulse area of Sa and negative pulses b' of the lower pulse width signal b are considered to be generated while the upper and lower pulse width signals a and b are as they are. Determining the frequency characteristics of the pulses a' and b' by the Fourier analysis, the areas of the pulses a' and b' are equal to each other, but the energy of the pulse a' is larger than that of the pulse b' as shown in FIG. 1C. As noted from FIG. 1C, the difference between the energies occurs in the range of high frequency, but the energies are generally equal in the range of audio frequency. Thus, it will be noted that if the time when the pulse a' is generated is not coincident with the center of the pulse b', then the positive and negative components fail to be completely offset, which causes the distortion or noise to occur. This also is true when the moving down from the upper bits to the lower bits occurs.